Practice Test 8 - AP Calculus BC

20 questions. Answer them in any order, then submit to see your score and every explanation.

For $g(x)=12x^3-5x+7x^2$ , what is $g'(x)$ ?
A curve is defined by $x=\tan t$ and $y=\sec t$ ; what is $\dfrac{d^2y}{dx^2}$ in terms of $t$ ?
Use the ratio test to determine convergence of $\sum_{n=1}^{\infty} \frac{n^4}{n!}$ .
For $x>0$ , minimize $f(x)=\frac{25}{x}+x$ . What value of $x$ minimizes $f$ ?
A continuous function $u$ on $[-3,1]$ satisfies $u(-3)=0.5$ and $u(1)=2.5$ . Does IVT guarantee a solution to $u(x)=1$ ?
If $s'(1)=0$ and $s''(1)=-4$ , how is the critical point at $x=1$ classified?
A telescope correction uses $\sum_{n=1}^{\infty}(-1)^{n+1}\frac{1}{n^2-1}$ . Does it converge?
Which integral gives the volume if the base is $0\le x\le 3$ , $0\le y\le 2x$ , with right-triangle cross sections perpendicular to $x$ ?
Based on this information, which of the following is the best estimate for the rate of change of the temperature, in degrees Celsius per minute, at time $t=5$ minutes?
An electrical signal is modeled by $V(t)=\ln\big((t^2+4)^3\big)$ . Which technique is most appropriate to find $V'(t)$ ?
Let $g(x)=\ln(x-5)$ . Which statement about limits best identifies the vertical asymptote of $g$ ?
A motion model is $v(t)=(t^2-1)\sin(5t)$ . What is $v'(t)$ ?
Region between $x=2y$ and $x=6$ for $0\le y\le 3$ ; square cross sections perpendicular to $y$ -axis: which integral is correct?
A tank's volume is $V(t)$ liters after $t$ minutes. What does $V'(12)$ represent in context?
A feedback process accumulates $\sum_{n=1}^{\infty} \frac{(-1)^n}{n^2}$ . Does the series converge or diverge?
A lab culture follows $\frac{dy}{dt}=1.5y\left(1-\frac{y}{200}\right)$ . Which value of $y$ is a stable equilibrium?
A circle's area increases at $12\pi$ cm $^2$ /min. When the radius is $6$ cm, how fast is the radius changing?
A velocity is given by $v(t)=\dfrac{\ln t}{t}$ . What is $v'(t)$ ?
Determine the interval of convergence of $\sum_{n=2}^{\infty}\frac{(x-1)^n}{n\ln n}$ for a convergence investigation.
What integral setup gives the area enclosed by $r=3-\cos\theta$ and $r=1$ ?

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